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Factors and Prime Factorization. 2.2. Finding the Factors of Numbers. To perform many operations, it is necessary to be able to factor a number. Since 7 · 9 = 63, both 7 and 9 are factors of 63, and 7 · 9 is called a factorization of 63. Finding Factors of Numbers. Practice Problems 1

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2.2

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  1. Factors and Prime Factorization 2.2

  2. Finding the Factors of Numbers To perform many operations, it is necessary to be able to factor a number. Since 7 · 9 = 63, both 7 and 9 are factors of 63, and 7 · 9 is called a factorization of 63.

  3. Finding Factors of Numbers Practice Problems 1 Find all the factors of each of the numbers. P 122

  4. Prime and Composite Numbers Prime Numbers A prime number is a natural number that has exactly two different factors 1 and itself. Composite Numbers A composite number is any natural number, other than 1, that is not prime. pp 122-123

  5. Examples Determine whether each number is prime or composite. Explain your answers. a. 16 b. 31 c. 49 Composite, it has more than two factors: 1, 2, 4, 8, 16. Prime, its only factors are 1 and 31. Composite, it has more than two factors: 1, 7, 49.

  6. Identifying Prime and Composite Numbers Practice Problems 2 Determine whether each number is Prime or Composite. p 123

  7. Prime Factorization Prime Factorization The prime factorization of a number is the factorization in which all the factors are prime numbers. Every whole number greater than 1 has exactly one prime factorization. p 123

  8. Examples Find the prime factorization of 63. The first prime number 2 does not divide evenly, but 3 does. Because 21 is not prime, we divide again. The quotient 7 is prime, so we are finished. The prime factorization of 63 is 3 ·3 · 7.

  9. Finding Prime Factorizations because 42 is not a prime number we must divide it by a prime number. because 21 is not a prime number we must divide it by a prime number. because 7 is a prime number we can now write the prime factorization of 84. p 124

  10. Factor Trees Another way to find the prime factorization is to use a factor tree.

  11. Finding Prime Factorizations 28 2 14 2 7 p 125

  12. Examples Find the prime factorization of 30. Write 30 as the product of two numbers. Continue until all factors are prime. 30 6 • 5 3 • 2 • 5 The prime factorization of 30 is 2 · 3 · 5.

  13. Examples Find the prime factorization of 36. Write 36 as the product of two numbers. Continue until all factors are prime. 36 9 • 4 3 • 3 2 • 2 The prime factorization of 36 is 3 · 3 · 2 · 2 or 32 · 22.

  14. Finding Prime Factorizations 120 2 60 2 30 2 15 3 5 p 124

  15. Finding Prime Factorizations 756 126 6 2 3 2 63 3 21 3 7 p 125

  16. Finding Prime Factorizations 70 2 35 5 7 p 125

  17. Finding Prime Factorizations 30 2 15 5 3 p 126

  18. Finding Prime Factorizations 56 2 28 2 14 2 7 Problem 7c: 72 and Problem 8: 117 p 126

  19. DONE

  20. Divisibility Tests

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